For the following definitions of forms/styles of communication I used Alcorn and Humphrey's, So You Want to be an Interpreter, as a reference. I picked key points that I thought would be beneficial to as many people as possible. The definitions chosen cover a wide variety of topics if you will, and are not necessarily in alphabetical order but more in category based order.
American Sign Language (ASL): only true language of the Manual Systems; a visual-gestural language incorporating facial grammatical markers, physical affect markers, spatial linguistic information, fingerspelling, as well as the signs themselves. Has its' own grammar and syntax, which is not derived from a spoken language.
Anglicized ASL: a form of signing which blends ASL with English based signs; a contact variety more closely affiliated with ASL than English.
Aural/Oral: language, which is based on a structured set of linguistic rules in which communication is based on sound.
Anglophone: a term used in Canada to refer to people who use English based communication, as compared to French-based communication.
Classifiers: a specific set of signs, which serve several functions in ASL. Some are iconic (look somewhat like the object they represent, such as "book") Others are arbitrary (there is no obvious reason for that sign or hand shape to be used as a classifier for the noun it represents). A classifier generally cannot be used until the noun it is representing has been signed. Classifiers can convey the relationship of a noun to a noun; the way a noun moves; and can describe a variety of nouns.
Real World Classifiers: classifiers that take on life size proportions and sometimes look a bit like a reduced form of mime when being produced.
Code Switching: the conscious or unconscious movement from ASL into English-like signing or from English-like signing to ASL; this often occurs due to the experience of oppression common to d/Deaf people in Canada and the U.S.
Contact Sign: formerly known, as Pidgin Sign English (PSE) is a term that refers to a contact language or blended form of English and ASL. Often used when d/Deaf people and hearing people attempt to communicate.
Sign Supported Speech (SSS): formerly know as Manually Coded English (MCE) invented manual codes used to represent the aural/oral language of English, accompanied by spoken or inaudible mouthed English which includes:
Rochester method: each letter of the English alphabet is assigned a handshape and all words communicated with the exception of "and" are fingerspelled.
Seeing Essential English (SEE1): is a code for English words where each syllable is given a separate manual movement.
Signing Exact English (SEE2): is a combination of SEE1, invented initialized signs, and some ASL signs.
Signed English (SE): combines grammatical order with ASL signs and some invented initialized signs.
Conceptually Accurate Signed English (CASE): combines English grammatical order with ASL signs and some invented initialized signs.